What is the current value per share at a discount rate of 14 percent?

Question

Martin's Yachts is expected to pay annual dividends of $1.40, $1.75, and $2.00 a share over the next three years, respectively. After that, the dividend is expected to remain constant at $2.00 per share indefinitely. What is the current value per share at a discount rate of 14 percent?

Answer 1

The value of a stock is equal to the PV of its expected future dividends. In this problem, we have 2 years of known dividends, followed by a known perpetual dividend after year 2. We need the sum of all 3 of those components to determine the market price per share.

To value the known dividend amounts for years 1 and 2, we simply use the formula for PV of a future cash flow:

PV = FV/((1+r)^n), where r is the rate of return and n is the number of years.

Thus, the PV of D1 is 1.40/(1.14^1) = $1.23. By repeating this calculation for the year 2 dividend and adding it to the year 1 dividend, we get a value of $2.57.

Next, we need to calculate the value of the perpetual $2.00 dividend. The formula for a perpetuity is:

PV = P1/r, where r is the rate of return and P1 is the amount to be paid one year from now. This gives us a PV of the perpetuity of $14.29 (2.00/.14). However, this is the value of the perpetuity when the $200 payment is one year away. In the problem, this payment is actually three years away, which means the value of that perpetuity is worth $14.29 two years from now. We need to discount the $14.29 back to present day value using the original PV formula. By doing so, we calculate the perpetuity to be worth $10.99 today.

To get the final value of the stock, we need to add the value of the perpetuity to the value of the 2 known dividends, which gives us an ultimate stock price of $13.57.